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Simplifying 2x2 + 3 + 8 = 33(2x) Reorder the terms: 3 + 8 + 2x2 = 33(2x) Combine like terms: 3 + 8 = 11 11 + 2x2 = 33(2x) Remove parenthesis around (2x) 11 + 2x2 = 33 * 2x Multiply 33 * 2 11 + 2x2 = 66x Solving 11 + 2x2 = 66x Solving for variable 'x'. Reorder the terms: 11 + -66x + 2x2 = 66x + -66x Combine like terms: 66x + -66x = 0 11 + -66x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5.5 + -33x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + -33x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + -33x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -33x + x2 = 0 + -5.5 -33x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 -33x + x2 = -5.5 The x term is -33x. Take half its coefficient (-16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. -33x + 272.25 + x2 = -5.5 + 272.25 Reorder the terms: 272.25 + -33x + x2 = -5.5 + 272.25 Combine like terms: -5.5 + 272.25 = 266.75 272.25 + -33x + x2 = 266.75 Factor a perfect square on the left side: (x + -16.5)(x + -16.5) = 266.75 Calculate the square root of the right side: 16.332482971 Break this problem into two subproblems by setting (x + -16.5) equal to 16.332482971 and -16.332482971.Subproblem 1
x + -16.5 = 16.332482971 Simplifying x + -16.5 = 16.332482971 Reorder the terms: -16.5 + x = 16.332482971 Solving -16.5 + x = 16.332482971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + x = 16.332482971 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = 16.332482971 + 16.5 x = 16.332482971 + 16.5 Combine like terms: 16.332482971 + 16.5 = 32.832482971 x = 32.832482971 Simplifying x = 32.832482971Subproblem 2
x + -16.5 = -16.332482971 Simplifying x + -16.5 = -16.332482971 Reorder the terms: -16.5 + x = -16.332482971 Solving -16.5 + x = -16.332482971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + x = -16.332482971 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = -16.332482971 + 16.5 x = -16.332482971 + 16.5 Combine like terms: -16.332482971 + 16.5 = 0.167517029 x = 0.167517029 Simplifying x = 0.167517029Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.832482971, 0.167517029}
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